RELATIONSHIP BETWEEN ZEROS AND COEFFICIENTS OF A POLYNOMIAL WORKSHEET

Problem 1 :

If α and β are zeros of p(x) = x² + x - 1, then find 1/α+ 1/β?

Solution

Problem 2 :

If one of the zeros of the cubic polynomial x³ + ax² + bx + c is -1, then what will be the product of the other two zeros?

Solution

Problem 3 :

If α, β, γ be zeros of the polynomial 6x³ + 3x² -5x+1, then find the value of α^-1 + β^-1 + γ^-1?             Solution

Problem 4 :

If α, β are zeros of the quadratic polynomial

f(x) = 2x² + 11x + 5

find

a) α⁴ + β⁴      b)1/α +1/β -2αβ

Solution

Problem 5 :

If the zeros of the polynomial f(x) = x³ – 3x² - 6x + 8 are of the form a-b, a, a+b, then find all the zeros

Solution

Problem 6 :

If α, β are the two zeros of the polynomial

f(y) = y² - 8y + a and α² + β² = 40

find the value of ‘a’?

Solution